Direction Fields, Euler Methods, Differential Equations

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Related lectures (27)

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Runge-Kutta Methods: Approximating Differential Equations

Covers the stages of the explicit Runge-Kutta method for approximating y(t) with detailed explanations.

Explicit Stabilised Methods: Applications to Bayesian Inverse Problems

Explores explicit stabilised Runge-Kutta methods and their application to Bayesian inverse problems, covering optimization, sampling, and numerical experiments.

Numerical Methods: Boundary Value Problems

Explores boundary value problems, finite difference method, and Joule heating examples in 1D.

Elasto-Gravity Bending: Energy and Equilibrium

Explores elasto-gravity bending in thin sheets, covering bending energy, equilibrium shapes, and numerical methods.

System of ODEs

Explores numerical methods for solving ODE systems, stability regions, and absolute stability importance.

Euler Forward Method

Introduces the Euler Forward Method for ODEs, focusing on error analysis and stability.

High Order Methods: Space Discretisation

Covers high order methods for space discretisation in linear differential systems.

Numerical Methods: Runge-Kutta Approximation

Covers the Runge-Kutta method for approximating solutions of differential equations.

Advanced Analysis II: Cauchy Problem Resolution

Covers the numerical resolution of a Cauchy problem using separation of variables and discusses the conditions for the solution's definition interval.

Finite Differences Method: Error Division and Schemes

Covers error division and schemes for solving differential equations.